I concur this is a 125A panel, with a limit of 70A per branch circuit (breaker) except for the mystery breaker, which can be 100A.
Once upon a time there was a "Rule of Six", which said you must be able to shut off all power by throwing no more than six breakers. Yours is indeed a "Rule of Six" panel but with three: the 2-pole breakers in positions 1, 2, and the (unnumbered) mystery position below 1.
It's very typical for a "Rule of Six" panel to use one of its six breakers (3 in this case) to power a "built-in subpanel" intended for smaller loads. That is what the mystery breaker does. Half-spaces #3 through #14 are the "subpanel". Together they cannot exceed whatever the mystery breaker's amp rating is, 50A I gather.
There is one code violation and several "urgent upgrades" called for.
Code requires you to obey all instructions and labeling (NEC 110.3). Your labeling plainly says position 1 can only be a 2-pole breaker that is full size, e.g. GE's THQL series, which note the panel label, is an authorized breaker type. What's in there is a THQP, GE's unique format of "double-stuff" 2-pole breaker where it straddles two spaces. This is a Code violation and you need to spend $9 on the correct full-size breaker. Since double-stuff breakers are not allowed here, I can only guess your panel cover doesn't have breakaways for them and you have a 1/2" gap above and blow that wrong breaker. Super not cool. Panels should never have open-space gaps.
The gaps can be corrected with GE-supplied blank covers, however I find those flimsy and prefer the meat of a real breaker (even if unused). GE's THQL breakers don't fit all older GE panels; if the THQL doesn't fit you may be forced into the obscure Eaton CL family of breakers, which is UL-Classified (approved) for this panel. (not Eaton BR). Find a real electrical supply that is an Eaton dealer.
Now I also am looking at the neutral bar and I see at least 6 neutral wires on small branch circuits where the wire is aluminum. Now aluminum is fine for the big feeders like your supply cable, because those tend to be installed with care. But for 15-20-30A branch circuits, aluminum requires very precise technique and properly rated terminations - and in the 1960s-80s, it didn't get it. Installers worked hastily and shabbily, and the industry didn't know about correct torque, No-Ox compound, Alumiconn splices, or CO-ALR terminations as they do now.
"OMG rewire my whole house" -- no. The usual failure mode of aluminum wire is series arcing. You can get special breakers called AFCI that detect and trip on series arcing. Put an AFCI on every aluminum circuit, then at your leisure make sure every aluminum wire ends on a properly aluminum-rated terminal - CO-ALR rated receptacles, Alumiconn splices etc. And use a torque driver to set the screw torque correctly. If they had done those things in the 1960s, there would have never been a problem. But they didn't know.
AFCI is a problem, though -- all your "subpanel" breakers are double-stuffs, and AFCI breakers don't come in double-stuffs (except for Siemens QP, which is not allowed in this panel).
So there is not room in this panel to replace six double-stuff breakers with full-size breakers.
If you can economize circuits, that's great. The two top breaker areas must be 240V breakers, but nothing says you can't put two independent 120V circuits on a 240V breaker.
Otherwise, my recommendation is a subpanel. The labeling says the largest branch circuit breaker you can use is 70A, so OK. Fit a 70A breaker in whichever position you can spare, either 1, 2, 3-4-5-6, (or 4-5 if you can find a double-stuff THQP270). Feed that over to a new subpanel. You are welcome to use another GE Qline panel if you prefer, make sure to get one rated for double-stuff (GE calls this Slimline) so you can reuse your existing breakers.
Then, reroute as many branch circuits as you can from spaces 3-14 to the new subpanel. I would aim for a subpanel location that let the old aluminum wiring reach the new subpanel without adding another splice to extend the aluminum wire. The copper circuits, feel free to splice them - no more than 2 circuits in a 4x4x1.5 box, no more than 4 circuits in a 4-11/16 square deep box.
Despite having many more breaker spaces, your house will still use the same energy as before, because you'll still turn the same stuff on.
Lastly instead of A/C, consider a heat pump or "mini-split". These are air conditioners, but are reversible - in cold weather they can chill the outdoors and blow the hot air inside your house, heating at well over 100% thermal efficiency, so you spend 1 watt to move 3-4 watts of heat into your house (or more depending on outside temp and SEER and COP rating). Notably, a heat pump takes 2 breaker spaces (one 240V breaker), whereas A/C and heat separates take typically 4-6 (at least 3 if the furnace is gas).